jycstudyfandomcom-20200214-history
Incentives in Teams
Why Teams? * Complimentary - foster coordination and cooperation in an organisation * Allows specialisation to occur and specialisation to be used to the max * But: ** Difficult to identify individual effort from the team effort ** Difficult to evaluate individual effort from team effort Pay for "Team"-Performance * Team Output can only usually be measured aggregately and individual effort is not seen * The externalities of teamwork is from the interaction between the team members ** Complementaries occur when the team works together and it benefits the entire team ** A team working together as a sum is better than the individuals ** One member putting in effort improves the team in general * This creates a problem of freeriding ** The actions of one individual benefits the group so this is the case of a private provision of a public good. ** Since the entire team benefits, some members of the team shall not contribute as they can benefit from the team effort itself. ** As a result, the team members that contributed will not be rewarded accordingly for the disproportionate effort they put in. ** Lack of coordination may also be a cause of free-riding as work is not distributed properly over the team members. First Best Effort(in partnerships) and reducing free-riding * Partnerships mean that output is shared among the team members * Output/Revenue is a1+a2+a3+....an * Cost per worker is 1/2*a^2 * Marginal team output dP/da = Marginal personal cost dC/da => Team-surplus maximising output * Suppose output is shared among the team by s1+s2+s3+.....sn = 1 * So a given worker's utility is = si(a1+a2+a3......an) - 1/2*ai^2 * Worker puts in the effort du/da = dC/da = ai = si * Whenever si < 1, worker will under-provide effort * Inducing first best effort to prevent freeriding would involve giving all of the profit to the workers which is not desirable ** Question solving ** the objective is finding a*, the optimum hours that the worker will put in as work ** Surplus is R - total personal Cost ** Maximise S to find optimum a* ** utility function is revenue share - personal cost ** For finding a* in a freeriding situation, we differentiate the utility function of the worker to find a* ** the utility function for this is the same, Revenue share - personal cost * Make pay system so that workers get paid only if they put in effort ~> Quota system * This makes each worker pivotal ** Question solving burning money: *** Worker utility function has two branches - one if the target is met and the other if the target is not *** If not met the utility will be 0 - personal cost. Otherwise it would be revenue share - personal cost. *** Revenue = (number of employees,n-1)*optimal worker hours + worker's working hour a *** Personal share would be above divided by 1/n *** Compare revenue share gained to personal cost to find best response *** Think slowly! ** Drawback of steep team incentives *** If everyone puts in one unit of output, the output will be shared completely among workers *** But if one worker puts in no effort, the output becomes n-1 *** The output is not there. What happened to it? Does it get destroyed? Are the nonworking members of the team rewarded with the output(Budget Breaking). *** Multiple equilibria - workers work as long as they believe the other will work *** Based on belief that others will work so if the belief is weak, worker will not put in work *** Weak self-enforcing equilbrium *** Budget Breaking as Debt Financing *** Firm takes a loan of D with a commitment to repay it with a guarantee (bonus?) of b to each worker *** D = n - nb *** If output is at least n, then firm repays D and pays each worker b *** If output exceeds n, excess is paid to workers equally *** If unable to make enough, bankruptcy and firm owned by creditor *** Bankruptcy ensures that work is done by the team members Pay for Individual and Group-Performance * How much to base compensation on group-performance or individual performance? * Individual performance better for measuring individual behaviour * Group performance allows individuals to take into account of their individual behaviour on the team * Pay on group performance may improve individual behaviour * RPE - Relative Performance Evaluation, performance of an individual evaluated in terms of another person's performance, promotes non-cooperation. Performance of others increase, pay of individual decreases. Used for: Benchmarking and Tournaments * JPE - Joint Performance Evaluation, performance of an individual evaluated in terms of the performance as a team, promotes cooperation. Performance of others increase, pay of individual increases. Useful for: Internalising externalities and fostering cooperation * Benchmarking ** Two risk averse workers exist P1 = a1 + e(common risk) and P2 a2 + e(common risk) ** Profit = sum of efforts = a1 + a2 ** Basing pay on individual effort/performance means worker bears risk ** Comparing each worker to average performance eliminates the risk P1 - (P1+P2)/2 ** Firm can induce first best effort in spite of workers risk aversion ** Comparing performance to others filters out common noise and infers lower risk to workers and increase individual incentives * Cooperation vs Incentive ** Paying for group performance incentivises cooperation and internalising externalities for the benefit of the group ** But since group performance is evaluated for individual pay, there is a possibility of free-riding ** Tradeoff between internalising externalities and free-riding ** Individual performances of P1 = a1 + ya2, P2 = a2 + ya1 ** Private cost = 1/2*a^2 ** Firm pays with individual performance APi and other team member performance BPj ** utility of worker 1, u1 = (A-B)P1 + B(P1+P2) - 1/2*a^2 ** firm pays B for joint performance and A-B for individual performance ** How would a worker change in individual and group pay? ** u1 = A(a1+ya2) + B(a1+ya2) - 1/2*a^2 = (A+By)a1 + (By+A)a2 - 1/2*a^2 ** worker 1 thus puts in effort A+By with individual pay increasing performance and group pay change effect depends on the externality Focused vs Broad based incentives * Read slides * TDR Broad based is better